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Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations

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Abstract

We show that ghosts in gauge theories can be interpreted as Maurer-Cartan forms in the infinite dimensional group ℊ of gauge transformations. We examine the cohomology of the Lie algebra of ℊ and identify the coboundary operator with the BRS operator. We describe the anomalous terms encountered in the renormalization of gauge theories (triangle anomalies) as elements of these cohomology groups.

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Author notes

  1. L. Bonora

    Present address: Istituto di Física dell'Università di Padova and I.N.F.N., Sezione di Padova, Italy

  2. P. Cotta-Ramusino

    Present address: Istituto di Fisica dell'Università di Milano and I.N.F.N., Sezione di Milano, Italy

Authors and Affiliations

  1. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    L. Bonora

  2. Lyman Laboratory of Physics, Harvard University, 02138, Cambridge, MA, USA

    P. Cotta-Ramusino

Authors
  1. L. Bonora
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  2. P. Cotta-Ramusino
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Additional information

Communicated by R. Stora

Research supported in part by the U.S. Department of Energy (DOE) under contract DE-ACO2-76ER03069

Research supported in part by C.N.R., I.N.F.N., and by the National Science Foundation under Grant PHY79-16812

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Bonora, L., Cotta-Ramusino, P. Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations. Commun.Math. Phys. 87, 589–603 (1983). https://doi.org/10.1007/BF01208267

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  • DOI: https://doi.org/10.1007/BF01208267

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